Superluminal velocities do generally not violate relativity, or help you to time-travel, or violate causality as long as there is only a single reference frame relative to which the propagation happens instantaneously. Yes, you read this correctly: even infinite velocity can be accommodated in Einstein’s relativity, and the necessary reference system could perhaps be as simple as a quantum tunnel barrier – no need to invoke exotic cosmology.

The pedagogic extra dimension example was mentioned because it is so very intuitive; lay people can plainly ‘see’ how faster than light propagation does not kill Einstein’s relativity. Let us investigate this today without extra dimensions. Just to remark quickly on the current relevance of all this: If, as was reported [1], neutrinos actually went faster than light from CERN to OPERA in Italy’s Gran Sasso, which I hold unlikely (yet not entirely unexpected for neutrinos), they can do so by involving short-distance phenomena many times faster than the speed of light without violating relativity or causality not only in case something jumps into extra dimensions but also if everything stays inside our usual three dimensional space.

I will start with the circumstances under which superluminal signaling does violate causality. Scroll through to the next section, section 2, if you are only interested in how this is resolved.

1) How Faster than Light goes back in time to kill Bob’s chances of dating Alice

The problem is the following: Alice is a really hot girl and has a crush on Bob, but of course only as long as Bob does not call her first. If Bob calls first, he will appear too eager for a date and totally lame in Alice’s mind. Now it is already 12 o’clock on Saturday and Bob is a popular hunk, so Alice better waits no longer; she sends an infinitely fast tachyon to Bob, meaning relative to Alice, the tachyon starts (event P) and arrives (event Q) both at twelve o’clock, that is t = 12h.

Alice sends a tachyon to Bob. Here, Bob does not move yet relative to Alice, which we will though soon assume.

The tachyon arrives at t* = 12h also relative to Bob’s clock showing time coordinate t*. Now consider that when Bob receives the tachyon, he happens to move away from Alice, speeding on the super freeway with half the speed of light or so. This implies that the tachyon started (event P) at time t*> 12h, perhaps at one o’clock relative to Bob’s current reference system: t* = 13h. There is nothing wrong or problematic with this yet, because time labels are first of all just that, labels, and you can easily understand why all this is true even without any formulas. This has been explained well enough merely employing pictures here, which is where I stole the above image.

Now where is the problem? The problem starts if on reception of the tachyon, Bob is allowed to perform the same procedure that Alice did, namely, he may immediately hit the answer button by accident and send the tachyon right back to Alice in the same manner as Alice did: The tachyon is starting (event Q) at t* = 12h and arriving (event R) instantaneously at the same time t*= 12h, too, but this time relative to Bob’s time t* because he is sending it. The situation is symmetric to that described before; Alice moves away from Bob because Bob moves away from Alice. No different from before, such implies that according to the receiver’s time coordinates, the sending happened one hour later. If the sending (event Q at t = 12h) happened one hour later, it must be now one hour earlier when receiving it (event R at t = 11h).

Alice started the whole business at t = 12h but she receives the answer from Bob before that at t = 11h. This cannot possibly be, because Alice is very attractive and would not send any message to Bob at all if he contacted her first and moreover at 11 o’clock on a hung over Saturday morning. Causality is violated.

Some conclude relativity is wrong; most conclude that superluminal velocities are impossible; both conclusions are mistaken.

2) Why Faster than Light does not mess up the Date

However, all hangs on one assumption: “The problem starts if on reception of the tachyon, Bob is allowed to perform the same procedure that Alice did, …”. “Same procedure” means here sending something instantaneously relative to ones own reference frame. If Bob can do the same, causality is violated. However, assume for example that Alice can only do so because she happens to be almost at rest relative to the cosmic microwave background (CMB), which is a rather special reference system left over from the big bang. In other words, the tachyon is instantaneous relative to the CMB. Bob moves away from Alice and thus relative to the CMB, therefore he can not send it back to Alice instantaneously relative to his own reference system.

One may equally consider that the instantaneous communication is bound to the membrane universe discussed last time, or say relative to the CERN muon reaction tunnel or even some telecommunication company’s private quantum communication tunnel device* which moves at any desired speed relative to the CMB (yet no possibility to have two such tunnels moving very fast close to one another without destroying each other). In all these cases, Bob sending the tachyon back will send it straight back from event Q to event P; it does not go back into the past.

(* Off the red thread Remark: According to many physicists, instantaneous quantum correlations may occur in the Einstein Podolsky Rosen problem. There, the one necessary unique reference system relative to which instantaneous ‘interaction’ may occur is – with much poetic license – the split where the many worlds interpretation’s multiverse branches. Be aware however that the recent resolution of the EPR paradox needs no faster than light correlations. In fact, I do not hold it likely that any of the measurements that hint at instantaneous quantum tunneling will hold up to scrutiny, but this is my personal opinion.)

There are two ways to understand all of the above better:

2.1) One way is to look at the so called light cone structure. The following illustration depicts a somewhat similar situation (not quite the one described above), namely one where there is also an event, here event E, that according to Alice is in the future but according to Bob is in the past. As you can see, while this would be completely impossible in Newtonian physics depicted to the left, in relativistic physics, not all past is already determined past (stuff that actually happened and is done with, decided, finished).

(a) Galilean relativistic Newton space-time, i.e. space, namely the x-direction, living through absolute time t = t*: The t-axis is Alice’s world line while the t*-axis represents the history of Bob. (b) Einstein relativistic Minkowski space-time: Bob moves with about a third of the velocity of light c/3 to the right. The event E occurs at t > t0 (Future) but at t* < t0 (Past) although both observers meet at t0 and synchronize their clocks then. (Illustration from reference [4], all rights reserved)

The determined past is inside the dark gray cone. Even if signals go forth and back with infinite speed along any of the x-axes, they cannot ever reach back into the determined past and change it (as long as they do it along the same x-axis and do not hop around between different reference frames).

2.2) The other way is perhaps the simplest, namely to imagine the universe to be like the surface of a pond of water. The following is adapted from the section “4.1. Causality preserving superluminal velocity but no time-travel” of reference [2]. It is a little long, so let me first point out two important points to keep in mind:

1) It mentions splashing water which invokes extra dimensions orthogonal to the universe that exists inside the pond's surface. This is only didactic and for example shock waves and sound can also travel through fluid much faster than the surface waves can do.

2) The main point is that the physics observable, the mathematical structure valid inside the fluid’s surface, is that of Einstein’s relativity. The conclusions (e.g. no time travel) hold regardless of whether or not the universe actually has such a fluid. All that is necessary is that superluminal signals travel at most instantaneously relative to a certain reference frame; obviously that does not need to be a pond of fluid. The fluid is a didactic tool just like the extra dimension, because when thinking about a fluid, no equations are needed to prove certain facts: We all take baths from time to time and thus we all know perfectly well that no wave or splashed drop can visit the water’s past, can somehow revisit wave patterns that simply do not exist anymore.

Considering a pond of fluid, splashed drops may reenter the surface after traveling above it with higher than the low energy wave speed c observed by observers living inside the surface:

Observers are made out of the waves on the pond and must choose as their “light” the fastest to them available excitations with few internal properties. Having no better measure, light must be used to measure light, thus it always has the same speed c. All objects are made out of simple waves trapping each other in patterns (pseudo particles). A pattern moving relative to the liquid’s molecules experiences time dilatation: A light-clock is a simple light wave bouncing between mirrors. If the clock moves with close to the speed of light, bouncing light needs much pond-time to reach the receding front mirror. The universe of these observers is special relativistic. A Minkowski space-time diagram suffices to establish that systems at rest in the pond also undergo time dilatation as measured from moving patterns (relativity)! The observers cannot measure how they are moving relative to the pond.

A mathematical model based on this picture is at low energies special relativistic inside the surface, yet allows faster than light phenomena that do not violate causality. The splashed substance carries at least the information that a high energy experiment has taken place. Superluminal information carrying phenomena need not violate causality if the signal travels at most instantaneous relative to the cosmological space-substance, i.e. it is tied to one and only one reference frame!

Since special relativity is valid inside the surface, there are inertial systems relative to which the superluminal splashing goes backwards in time, but in none does it splash into their past light-cone (which is their causal past). No equations are needed to prove it: We all take baths and know that no wave or splashed drop visits the water’s past. Imagine you stand next to a pond watching some sentient beings made from the pond’s surface waves: the futility of their efforts to invent a time-machine is ridiculously apparent. A space-substance giving rise to general relativity in as far as it is confirmed by observations renders the idea of time-travel equally ridiculous: Excitations of a substance cannot visit a previous state of the substance that plainly does not exist anymore. Deriving such results as far as they apply to special relativity from an abstract viewpoint that refuses to consider fluid ponds needs many pages, equations and diagrams [3]. It is basically impossible to do so didactically for general relativity.

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[1] OPERA Collaboration: “Measurement of the neutrino velocity with the OPERA detector in the CNGS beam.” arXiv:1109.4897v1 (2011)

Comments

Very nicely explained, now I understand it much better - thats hould also help me make sense of the SME-models with superluminal neutrinos.
BTW, the english name of my blog (thanks for the praise) is "Here there be dragons"

Aren't you German? I haven't taken a German class since high school but it makes no sense to me. I have never seen hier as 'here' and 'there' at the same time. Is that a clever Schroedinger hier he has?

The English name for the blog does not contain a direct translation of the German verb wohnen, which means to dwell or reside. (Try typing it into http://dict.leo.org to get a fuller range of meaning.) The cognate verb is found in Middle English, in Chaucer:

However, there certainly be “tygers” when trying to cross linguistic swords with Sascha. Though I seem to have got away unscathed when dealing with the origin of the term "Pommes Frites". There is a lovely little poem which states that the name originates from their introduction to Germany by Frederick the Great of Prussia, aka “Old Fritz”.

D´rum heißt sie auch, das ist kein WitzPom Fritz

Therefore they are known, no joke,as Pom Fritz

However, I in my British way read the last bit as referring to the man himself:

A light-clock is a simple light wave bouncing between mirrors. If the clock moves with close to the speed of light, bouncing light needs much pond-time to reach the receding front mirror.

Is this a simplified view(dumbed down) of what's happening? Or is it analogous excepted in a different 2-d medium?

This pond of fluid, is much how I view the propagation of light. To me, I see the clock change how it measures time, not the rate of time changing. In fact (right or wrong), it was these types of things that confuses me, it's obvious (to me) the clock is the problem, not time, and always the answer was it was time that slowed.

A mathematical model based on this picture is at low energies special relativistic inside the surface

This is an analogy, and appears to be rather similar to Hendrik Lorentz's attempt to "explain" (the FitzGerald-Lorentz explanation) how the speed of light appeared to be independent of the reference frame, within the confines of Galilean (Newtonian) relativity.

This is neither a simplified version nor an analogy, this is the exact reason for why relativity emerges in condensed state systems. If it were not exactly like this, time dilation would not have the same dependence on relative velocity, which would immediately imply that you could easily find out (from inside the surface) what your absolute velocity (relative to the pond) actually is. The whole problem with relativity is that you cannot find any preferred reference frame, and so you do not know whether there is one and may (orthodox GR) conclude that there is none even on principle.

At high energies, the "splashing" might occur (think of ocean rogue waves colliding/breaking, solitons, shock waves) and tell you where the cosmological reference frame is, if there is one. This is perhaps what happened now at CERN, perhaps.

Let's not forget Alberts father was an engineer responsible for the swiss railway stations clocks (which you can still wear on your writch thanks to Swatch). Only when then the swiss trains went into operation it was necesserary to have a national or global time. Albert thought on and defined a universal time, but it's still only swiss. I love Swiss station clocks.

Many papers on superluminal speed and all that, many many, and I am aware of them and why I do not reference most. If there is too much weaseling like in too many microwave papers, then it backfires, even if correct. I like clear cut convincing arguments and none of this throwing around phase versus group velocities including every experiment indicative of superluminal phenomena (most of them are total rubbish) blowing up a paper to 50 single spaced pages. Life is too short ;-)

Breaking the speed of light limit, even as it preserves causality is a big deal conceptually. Yet the speeding ticket is tiny, one part in ten to the five. Do the extra dimensional or what you discussed here give a reason for the small bump above c? I recall you putting in numbers by hand so that things work out, but that is different from having a reason why the speed up is small. In addition, I would think there would be an entire range of speeds the neutrinos could travel. It would be interesting to know the distribution of the measurement of the neutrino speeds, wether that would tell anyone brighter than I clues.

This is assuming constant speed. Given the supernova neutrino measurements (sub-luminal velocity), the phenomenon indicated is one that has many times the speed of light (relative to CERN) but only for about 20 meters around the neutrino creation.

At very high superluminal velocity V above ~ 10 c, the distance of superluminal propagation isx = c * t where t is the 60 ns early arrival. At lower superluminal velocity use:

x = c * t / [1-(c/V)]

V = 10 c to infinity gives x = 20 to 18 meters (note that the difference here is close to the 3m uncertainty in the data), while V = 1.2 c gives 100 m, and your assumption gives 730 km. An average distance x of tens of km would likely result in fuzzier data (depending on the assumptions about the 're-entry' mechanism). The data being not smeared out that much and also the expectation from condensed state physics emergent relativity both point towards very high velocity over a small distance.

I've seen you use the term "condensed state physics" (with some variation) a number of times, thus far. I'm not certain whether you are using the term to mean what it more commonly means within the wider physics community (namely condensed matter, solid/liquid state, basically states of matter—within our universe—that are not gases or plasmas), or if you are using the term to mean some quantum theoretic (or beyond) "condensation" of quantum states (of some kind) into some emergent "space" of some sort.

Both, as CSP applies to both. Emergent relativity has been confirmed in several condensed state systems (graphene, super fluid helium, crystals). Relativity is SO(d,1) group symmetry, which is quite expected with d-dimensional condensed state systems. Particle physics (standard model, Higgs condensate, string theory) and gravity (Einstein-ether) look very much like CSP, so much so that it is almost beside the point whether there 'really' is a fundamental condensate, because such questions are almost a matter of taste.

To those who say "well come on, you know very well there is truly really fundamentally actually not" I can only say that neither is there "truly really fundamentally" any water or ice either. Concepts like "condensed state" are fundamentally our ways of describing observed phenomena.

I just noticed that you posed this question under my comment stating "... condensed state physics emergent relativity both point ...". By that I mean that if you look at the limit velocity of pseudoparticles in super fluid helium for example (Landau limit 58 m/s, 46 m/s measured for 4HeII, above this velocity, super fluidity breaks down) and compare it with the limit velocity of helium outside of the superfluid helium (basically the light velocity), then the difference is a factor of 299792458/50. If that is any indication at all, expect the neutrinos to be able to go at speeds of 10000000 c !

"However, assume for example that Alice can only do so because she happens to be almost at rest relative to the cosmic microwave background (CMB), which is a rather special reference system left over from the big bang."

You're assuming for your hypothesis that the CMB constitutes a special frame of reference. Based on the Principle of Relativity, which gives rise to the Special and General Theory of Relativity, there are no preferred reference frames; the laws of physics are identical regardless of the frame of reference. If the CMB delineated a preferred reference frame, it would be as significant a violation of the Theory of Relativity as FTL neutrinos.

Forgetting about the imaginary ansible and talking about the suggested faster-than-light neutrinos, this "solution" creates bizarre physics issues. If you have a ship with a rotatable FTL neutrino source and detector, moving at relativistic speeds, you would observe from that reference frame that FTL neutrinos are sped up as they are beamed away from the direction of motion and slowed down as they are beamed forwards. If you also have an ordinary neutrino source and detector, you observe no such difference. A force from a field external to the ship does not even explain the change in speed, as a force would cause an acceleration or deceleration, when what is observed is just an instantaneous change in velocity.

You're assuming for your hypothesis that the CMB constitutes a special frame of reference.

No I don't. I clearly took this as no more than one of several examples (the one easiest to understand to lay people)

Based on the Principle of Relativity, which gives rise to the Special and General Theory of Relativity, there are no preferred reference frames;

No, SR implies that there is no way to find any preferred reference frame (this does not even hold anymore in GR). Relativity means that you cannot say whether or not there is such a frame, which is pretty much the opposite of what you claim.

About the rest: You assume constant velocity. The data indicate a short distance of about 18 meters of ultra high velocity followed by sub-light velocity after 're-entry'.

It kind of makes you wonder, if you can lob a neutrino above the fabric of space-time, what else can you throw? Hopefully without breaking it.

Also, am I getting this right - according to Sasha's possible interpretation of these results, in principle person A could (virtually) instantaneously message someone, person B, who then instantaneously messages back after a short period processing this signal.

The time difference measured at the original sender is just the processing time (measured at B, then scaled lorentz-style to get an equivalent measured time at A), which could be short enough so that light wouldn't even have reached person B yet. The lorentz transformtions would just describe the motion of anything light-like or measured using electromagnetics (which in reality are the only things really limited to light speed, as so far it is only light that has been shown to have constant speed relative to the emitter).

Thus some device used to measure the effect of the super-luminal message at person B would have no idea anything had happened at B, because it takes that long for the information to travel back through space-time. This preserves the effect of all the experiments done so far validating SR. However, some time later, you could detect the message arriving at B, but at some point in the future (seemingly violating causality, because you see the message arriving at B after you get your reply, but really it's just your detector being slow).

All this of course requires some universal 'time' which cannot even in principle be measured because all our clocks are EM based (even pendulums and mass-spring systems, as they rely on forces transmitted through rods and cogs, which are EM).

All this of course requires some universal 'time' which cannot even in principle be measured

Keep in mind that signaling with such a method (if possible at all) would be extremely difficult and perhaps only possible over quite short distances, thus hardly getting much of an advantage out of it. However, if any such thing is possible, this would of course be the very means to access an (otherwise non-existent or plainly hidden) universal time.

What? No smack-down of some minuscule error I've made?!?! Either it is my lucky day, or you are on an off-day!

Your explanation seems to be consistent, which is nice. I'm almost hopeful that it's correct and there is some new realm or something which we are just starting to get evidence for. Of course actually building such a communication device is well beyond our current grasp, but it's all about the fundamental principles, isn't it?

Because if you 'change Alice to CMB', Bob cannot also be so changed.Causality violation can only happen if the situation is symmetric in such a way that both can send the signal back into the (to the other one) relative past, because then it enters the past light cone (the determined, causal past).

So the reasoning is: Alice first sends a simultaneous signal to Bob (Bob receives it at the same time Alice send it in Alice timeframe), then Bob sends a simultaneous signal back to Alice: Alice receives it at the same time as Bob emits it in the Bob timeframe, but that time in Alice frame is prior to the time Alice emitted the first signal: causal violation. Until here I understand.
Now, Alice occupies CMB reference frame, which is "allowed instantaneous information transfer" and is the only one, and she does as before. But now Bob cannot answer the same because he's moving from Alice (CMB) so he's not at CMB frame and then cannot send the simultaneos signal.
So in the first example, every reference frame (Alice, Bob...) were allowed the emission of tachyons, but in the second example only CMB frame can allow that. In other words, tachyons only exist from the viewpoint of the CMB reference frame and in that way causality doesn't get violated.
Did I get it correctly? Is that the standard interpretation of the CMB frame or is part of a new set of ideas?
Thanks for your patience!

Unfortunately, Enrique, there is one little "nit to pick" in you concluding remarks. You said:

So in the first example, every reference frame (Alice, Bob...) were allowed the emission of tachyons, but in the second example only CMB frame can allow that. In other words, tachyons only exist from the viewpoint of the CMB reference frame and in that way causality doesn't get violated.

However, even in the second example, every reference frame is still "allowed the emission of tachyons", and, so, "tachyons exist" in all reference frames. The difference is not an "allowed" vs. "not allowed" or "exist" vs. "not exist", but what velocities such tachyons are allowed to have, relative to the reference frame in question, since the allowed tachyons, for all of space-time, are those with velocity up to infinite relative to the CMB.

Within other reference frames (besides Alice's) one may emit tachyons that even move "backward in time", relative to that reference frame, so long as the direction of emission is in the direction of motion of the reference frame with respect to the CMB (or, equivalently, opposite to the direction of CMB motion, relative to the reference frame).

However, you are most certainly correct that this restriction upon the velocities of tachyons, relative to one particular reference frame (the CMB, in this case) is what prevents a violation of causality.*

David

* Now, whether such is a violation of the principle of relativity (and by that I don't mean Special Relativity, but a far more general principle that was known even by Galileo) is a whole nother question. However, such principles are human constructs, that Nature has no obligation to follow. ;)

Yes, Sascha, it does bear repeating that such an interpretation of the CMB reference frame (thus making it a special and/or preferred reference frame) is most certainly not a "standard interpretation".

Personally, I'm much more inclined to "gravitate" toward the Principle of Relativity that to require Causality (if I had to choose between them, because I prefer both). However, as a scientist I have to recognize my own bias in this matter, and always remember that it is Nature that is the ultimate arbiter, not any human preferences. (Human preferences are allowed to play a part when choosing between alternate explanations that cannot, at least for the time being, be distinguished via experiment/observation—but past that, the "ground truth" is in matching experiment/observation.)

Hi Sascha. As a layman, I'm not sure what the point about the CMB is. The CMB was produced by non-relativistic plasma which evolved into the universe as we know it, in which most ordinary matter is non-relativistic too. This is inevitable for cool massive particles. This gives us two grabs at the same centre of momentum frame - the plasma back then and massive objects right now. (They should be the same unless we are hurtling through space or the plasma was. The CMB just lets us measure such movement.) As you are presumably,not proposing new physics on the actual microwaves or plasma, there doesn't seem to be any point in introducing a phenomenon that links the two. Why not just point out that most objects, including CERN and Gran Sasso are, in relativistic terms almost at rest relative to each other, and that this implies there is (for actual objects if not for Lorentz transforms) a universal rest frame?

Just pointing out that there is a unique rest frame lets many unsatisfied, because they want to have at least one intuitive example of "how it actually may work". The CMB suggestion is such an example.Do not regard the CMB too lightly. Those who defend orthodox relativity are often dogmatic about that there is absolutely no way that any reference frame at all ever could possibly be special in any way. If however that were true, there would be no way in which the early universe could have ever broken that symmetry and put the CMB in a certain frame. After all, the CMB is in the frame that it is in and not in any of the infinitely many others. An upright pen can fall over into a random direction, because that pen has a constant probability distribution over all angles. If you try similar in special relativistic space, it does not work, because all probability is stuck in the frame that goes with light velocity (think about it - the probability distribution must be the same for all frames!). There would never be any matter at all if you really tried to do everything completely Lorentz symmetric. That first particle that chooses the CMB could be called "God particle" if any deserve such a name, ha ha.

Hmm. That rather reinforces what I was saying. You are calling something which has existed since the Planck time "the CMB" which came much later and the cause has now gone. Lay people certainly want to know "how it works" but if you don't remind them that the CMB just one way of observing the rest frame, they will get the vague impression that's there's something funny about the microwaves themselves which turns them into a tachyonic aether.

Anyway, my pedagogical misgivings aside, you have conducted me to the early universe where there are no particles (or just a parallel luxon bundle) and it is all symmetrical. What does that leave? Energy would have to be entirely contained in invariant scalar fields. Now, there's an idea!!!

And then the first, "God", particle appears and creates a subluminal frame. But if another one comes along, a new frame appears challenging the divine authority of the first and playing havoc with probability distributions. So perhaps the second particle was the devil particle. The point being, the first particle's frame is not special unless it's the only particle around when, unremarkably it is. But even then, there is a problem - why should a probability distribution suddenly be the same at all locations -even where they are not causally connected? Or does the particle sit in the middle of an expanding bubble where things can happen, thus raising the question of what is actually propagating?

Surely it makes more sense to say relativity space *must* be augmented with a datum frame even if it's totally empty.

Sorry if this is a load of ** - I was advocating explaining the rest frame in terms of contemporay massive objects, not going back *before* the CMB plasma but I guess "going back in time" is appropriate for a discussion about FLT sigalling :)

but if you don't remind them that the CMB just one way of observing the rest frame

well, I tried to remind about a million times that this is only one example anyway. Also: I would never call it "The rest frame"

they will get the vague impression that's there's something funny about the microwaves themselves

That danger exists, but this article is talking to a science educated audience. The CMB is well known there, and if I would use some Planck stuff instead, it would just sound silly. CMB is observed while Planck stuff ...

I was advocating explaining the rest frame in terms of contemporay massive objects

Yes, as I wrote, the CMB frame is the same as the average star background. But this does not help people understand the important issue: many dogmatic 'skeptics' implicitly claim that this unique frame is no more relevant than any imagined rocket spaceship. These people often do not grasp that general relativity is less "relative" than special relativity. "General" means localized, but this implies cosmology (= CMB).

Well, it was you who brought the early universe up, though I'm very glad you did as I now see that the "skeptics" have set themselves the task of creating invariant versions of every physical quantity. Something like the inverse transform but without referring to the originating frame. It sounds trivially impossible but presumably they know something I don't, which wouldn't be hard. It's the middle of the night here, I am going to sleep on it, so thanks for the nudge in the right direction!

Sascha, it seems to me that you make this sound more complicated than necessary. Physics is causal as long as it's causal in at least one reference frame. Faster than light particles would spoil relativistic frame invariance, but not causality.

In a sense, you are correct, however, if you say "would spoil relativistic frame invariance", you will have an army of people telling you that this is all there is to relativity, i.e. if you do not have this, then relativity would be wrong and we would get different experimental results. You have to go through some explaining in order to get people to understand that relativity would be pretty much untouched.

With a very weakly interacting FTL particle it would be hard to measure any difference. But if the FTL particle were significantly involved in ordinary chemical interactions then the laws of chemistry would not be frame invariant, and so it could be that biological processes (including us) would stop working if we moved too fast.

I like to explain the time and distance and the speed of light.
Distance CERN and Gran Sasso 730 km. Time straight line 10.500 nanosec. In seconds this is 0.0024 . 60 nanosec before Gran Sasso takes 18 meter. Speed of light 300.000 km/sec.
You can’t faster go then 300.000 km/sec. 730/300000=0.0024sec.
The straight line is 730 km is impossible to go by the neutrinos because of the gravity caused by earth. The neutrinos must take a bowed way .The straightway is impossible to go.
10.440 + 60 = 10.500 nanosec.= 0.0024 sec.
Cern.-----------------------------------------------------------------------…………. Gran Sasso. 10.500 nanosec.
730 km (straight way is impossible) + 60 nanosec.18 m= bowed line.
When the neutrinos arrive it look like they went faster the speed of light, because of the distance 10440 in the straightway, but they took the bowed way and this way was 18 meters longer! The real way was made by the speed of light C=300.000.
730+18 m./300000=10500 = 0.0024 sec. bowed distance/C=time)
You have to calculate with the real (bowed)way 730+18 m. the neutrinos made and not the (straight)distance 730 km. from CERN and Gran Sasso!
So Einstein is still alive! His point of view the speed of light is approved and the gravity of the earth has a CERN-machine to calculate with the gravity from Geneva CERN to Gran Sasso.

I don't see it breaking the constant, 'c'? And if it doesn't then the constant still is there. 'Tunnelling' is, to me, not about 'speed' at all, although I know there are people wanting it, as well as defining it, as going FTL. Tunnelling reminds me more of a entanglement, although, only involving 'one particle',

How is it that everyone thinks that there can be some "instantaneous communication" all of the sudden. For instance if I snap my fingers, travel faster than the speed of sound in any direction I would be able to HEAR my finger snap and I could even snap a second time at the same time but I won't be able to see myself snapping. Just is this with the speed of light. You can go out in space in any direction with infinate speed and look back at earth and see how it was but if you were to communicate with it you'd be reversing the "light time" that you just backed up. And it would reach your "twin" or whoever at present "earth time" minus the time it took to travel. The time could be very very small but not zero or negative. All of the "bending" just has to do with mathmaticall inaccuracies. Taking the trip home would just put you in a course with getting back to the present time on earth. Passing earth would just go to present and then back again on the other side. It's more of a "sight travel". Any correspondance back to the originating will reverse the apparent time of the space man and catch back up to current earth time when it arrives. The only question that I can thing of is; What does the object that travels at the speed of light look like from behind? You'd have to travel behind it in order to see it but during acceleration would it flash? Breaking the speed of sound causes and audible boom, so breaking the speed of light should be a visable flash right?